Question : Two tourist buses start from the same point and move along two roads at right angles at speeds of 48 km/hr and 36 km/hr, respectively. The distance between the buses after 15 seconds is ________.
Option 1: 175 m
Option 2: 350 m
Option 3: 250 m
Option 4: 150 m
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Correct Answer: 250 m
Solution : Speed of Bus A = 48 km/hr = $48×\frac{5}{18}=\frac{40}{3}$ m/s Speed of bus B = 36 km/h = $36×\frac{5}{18}=10$ m/s Distance covered by bus A in 15 sec ⇒ Distance = $\frac{40}{3}$ × 15 = 200 m Distance covered by bus B in 15 sec ⇒ Distance = 10 × 15 = 150 m As the two roads are at a right angle, so ⇒ Let Base = 200 m and Height = 150 m Here, Hypotenuse = Distance between two buses By Pythagoras theorem Hypotenuse2 = Base2 + Height2 ⇒ Hypotenuse2 = 2002 + 1502 = 40000 + 22500 = 62500 ⇒ Hypotenuse = $\sqrt{62500}$ = 250 m Hence, the correct answer is 250 m.
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Question : Vinay and Mahesh are 250 metres apart from each other. They are moving toward each other at speeds of 36 km/hr and 54 km/hr respectively. In how much time will they meet each other?
Option 1: 12 seconds
Option 2: 20 seconds
Option 3: 10 seconds
Option 4: 15 seconds
Question : In a circular race of 4225 m, X and Y start from the same point and at the same time, at speeds of 54 km/hr and 63 km/hr, respectively. When will they meet again for the first time on the track, when they are running in opposite directions?
Option 1: 140 seconds
Option 2: 150 seconds
Option 3: 130 seconds
Option 4: 120 seconds
Question : Two trains start from a certain place on two parallel tracks and in the same direction. The speeds of the trains are 45 km/hr and 40 km/hr respectively. The distance between the two trains after 45 minutes will be:
Option 1: 2 km 500 m
Option 2: 2 km 750 m
Option 3: 3 km 750 m
Option 4: 3 km 250 m
Question : The speeds of a boat along and against the current are 14 km/hr and 8 km/hr, respectively. The speed of the current is:
Option 1: 11 km/hr
Option 2: 6 km/hr
Option 3: 5.5 km/hr
Option 4: 3 km/hr
Question : In a circular race of 1600 m, A and B start from the same point and at the same time at speeds of 27 km/hr and 45 km/hr, respectively. After how long will they meet again for the first time on the racetrack, when they are running in the same direction?
Option 1: 90 seconds
Option 2: 320 seconds
Option 3: 240 seconds
Option 4: 180 seconds
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